Edgar never had a drain. The BP had a lip around the edge to form a pan. I just scraped the grease out after a couple cooks or sometimes put in fin foil and rolled it up and threw it away.
That much gap on each end of the BP is fine. I used to run Edgar on 1/4 of that size.
Your idea of the 3/8 plate needs to be there anyway - regardless of the gaps or you WIll have a hot spot in the center.